 # P/E Ratio

guys, I know we’ve discussed this before, but I’m still not sure what the resounding opinion is and I also can’t find the relevant thread. So what’s the impact on the P/E ratio when dividend payout increases? thanks.

Lola, ROE X Retention Rate = Growth. When the a company has a low ROE payout should increase because they don’t have profitable opportunities. If ROE is high then payout should decrease. Plug in some numbers and you will tell which way the P/E is moving… D1/(K-G)

I remember denominator dominates in this case. So P/E will decrease. Yes. Probably just use some number to prove it.

the answer is INCREASE the way i remember it is: P = D1/(k-g) now, divide both sides by E1 P/E1 = (D1/E1) / (k-g) so, you can see how the P/E ratio is directly affected by dividend payout ratio (D/E)

I read somewhere that change in g has the greatest impact on P/E, k (rate of return) has the second greatest impact, leaving the numerator (dividend payout) with the least impact (g>k>D). That being said, if the dividend payout increase, the retention rate will decrease, which will then decrease the growth rate. the decrease in growth rate will widen the spread of the denominator which will cause the P/E to decrease.

There is another factor to be considered which was discussed in a couple of threads a few days ago. The actual Increase or decrease is actually defined by the ROE and Ke relationship. If ROE > ke --> Retaining earnings is better than any new project (new equity) that the company might generate. In this case – increasing k (dividend payout) might actually end up reducing the P/E ratio. If ROE < ke --> Then increasing K would increase the P/E ratio.

Dividend payout increases, RR decreases restate g=RR*ROE=(1-Div)ROE where div=dividend payout ratio P/E=Div/(k-(1-Div)(ROE))=Div/(k/Div - roe/div+roe) =1/(1/Div(k-Roe)+Roe) if k>ROE, and Div increases, then denominator smaller, P/E larger if k

hmmmm great points, i’ve honestly never really considered them before… so what happens in the exam? is there a hardset rule about what does what? cos in every prac question that i’ve done, i’ve always assumed increase in dividend payout increases the p/e ratio (im sure) what about if i restate the question… what impact will an INCREASE in dividends have on the PRICE? it will obviously increase it right?

if you increase dividends at the expense of your growth rate (by increasing the payout ratio), then that may not be the case honestly I don’t know and am not inclined to go any further tonight there could be a situation where a judgment call has to be made between what they’re likely asking for from a common sense perspective, vs. what might actually be right from a pure math perspective… I noticed this a couple times in schweser, but am 99% sure CFA has their t’s crossed i’s dotted a lot better, so it’s not something to really worry about in my opinion.

cpk123 Wrote: ------------------------------------------------------- > There is another factor to be considered which was > discussed in a couple of threads a few days ago. > > The actual Increase or decrease is actually > defined by the ROE and Ke relationship. > > If ROE > ke --> Retaining earnings is better than > any new project (new equity) that the company > might generate. In this case – increasing k > (dividend payout) might actually end up reducing > the P/E ratio. > > If ROE < ke --> Then increasing K would increase > the P/E ratio. This is a nice explanation. I remember encountering this prob. in L-I myself.

Agreed cpk’s explanation is the way to go for such questions

Yes. cpk and dimes are right. Nice job. For ROE > k, let k = ROE -c; c > 0. You can reduce the P/E formular to 1/(ROE - c/DPR); where DPR = 1-RR. For ROE < k, let k = ROE+ c; 1/(ROE+c/DPR). For ROE = k, p/e = 1/ROE; stay constand regardless of paymen ratio change.

These excerpts are noteworthy and may provide some additional insight. Reducing k is addressed, but it would have been helpful if CFAI had discussed it w/in the context of ROE. This example also pertains to initiating a dividend, rather than just increasing an existing dividend. 2008 CFAI LII Curriculum: Volume 3 (Corporate Finance), Reading 33: Dividends & Dividend Policy: Section 6.2: Dividends Matter: Investors Prefer Dividends, p.177-178. Example 10: Dividends and P/Es Splashco Inc. is an international oil service company headquartered in Calgary, Alberta, Canada. It has a good record of earnings growth over the last 20 years, albeit subject to the ups and downs of oil and gas production. It has never paid dividends but has used its considerable cash flow to repurchase shares. Institutional investors in both Canada and the United States have indicated that they think Splashco would sell at a PE multiple more similar to its competitors if it instituted regular dividend payments. John Petrowitz, CFA of Splascho’s Treasurer’s office has been asked to present the case for a dividend to the company’s Board of Directors. He stars his analysis with the fact that Splascho typically sells at a P/E of 12-15x current earnings per share as compared to 17-20x for its competitors. He decided to use the constant growth dividend discount model to make his case. P = D1/(k-g) Dividing both sides of the equation by E1, where E1 = next year’s estimated EPS, the result is P/E1 = (D1/E1)/(k-g) Constant growth is estimated at 8 percent. The implied required rate of return for Splashco has been 12 percent, but Petrowiz thinks the initiation of a dividend would lower the required rate of return to 11 percent, close to the average of its competitors. If Splascho had a target payout ratio of 50 percent and next year’s earnings were C\$2.00, the P/E1 would be P/E1 = (1.00/2.00)/(0.11-0.08) = 0.50/0.03 = 16.7x Petrowitz concludes that if Splashco initiated at C\$1.00 dividend, it might alleviate some investor concern about what the company would do with its earnings and its P/E might increase from 12-15x to 16-17x. p.182: According to those who argue that dividends do matter, a company could increase its P/E ratio by initiating a cash dividend. The initiation of a dividend results in a higher P/E by reducing the spread between the company’s required rate of return and its expected growth rate using a constant growth dividend discount model.

thanks, all. cpk123, that’s exactly what I was wondering when I was typing the post. I remember there being a relationship between k and ROE, and I’m glad you all explained it so lucidly. much appreciated.

If all else is held constant then d1/(k-g) > numerator increases > P/E increases In actuality, as the other guys said, market perception about dividends is that the company is unable to find ways to grow so it is handing out the profits back to its shareholders. This lowers g and therefore the denominator increases > P/E decrease

cpk123 answered this correctly, but I just came across this material again and wanted to share the following excerpts from CFAI for those who are interested. It’s a long read but maybe worthwhile to the inquisitive. Everything that follows is quoted. 2008 LII CFAI Volume IV, Reading 40, p.148-150 “Using the DDM as a representative model, Leibowitz and Kogelman (2000) developed the franchise value method and separated the intrinsic P/E value of a corporation into a tangible P/E value and the franchise P/E value (derived from prospective new investments). The franchise P/E value is related to the present value of growth opportunities (PVGO) in the traditional breakdown of intrinsic value into the no-growth value per share and the present value of growth opportunities.” “In that breakdown, the no-growth value per share is the value of the company if it were to distribute all its earnings in dividends, creating a perpetuity valued at E1/e, where E1 is next year’s earnings and r is the required rate of return on the company’s equity. Using the DDM and the company’s actual payout ratio to generate an intrinsic value per share, P0, the present value of growth opportunities must be the difference between intrinsic value and the no-growth value per share, P0 - E1/r.” “The franchise value approach focuses on the intrinsic P/E rather than on the intrinsic value P0; thus, the franchise value P/E is PVGO/E1. In the franchise value approach, however, the franchise value P/E is further broken down into the franchise factor and the growth factor. The growth factor captures the present value of the opportunities for productive new investments, and the franchise factor is meant to capture the return levels associated with those new investments. The Sales-Driven Franchise Value has been developed to deal with multinational corporations that do business globally (see Leibowitz, 1997, 1998).” “The separation of franchise P/E value into the franchise factor and the growth factor permits a direct examination of the response of the intrinsic P/E to ROE[footnote 17]. This factor helps an investor determine the response of the P/E to the ROE expected to be achieved by the company. It focuses on the sustainable growth rate of earnings per share. Earnings per share will grow from one period to the next because reinvested earnings will earn the rate of ROE. So the company’s sustainable growth rate is equal to the retention rate (b) multiplied by ROE: g = b*ROE. Substituting into Equation 40-3 the sustainable growth rate calculation for g, we get the intrinsic P/E” P0 = E1(1-b) / r - b*ROE and converting to an intrinsic P/E ratio, P0/E1 = (1-b) / r - b*ROE Now, multiplying through by r/r yields P0/E1 = 1/r [r(1-b) / r - b*ROE] = 1/r [r - r*b / r - b*ROE] and arbitrarily adding and subtracting ROE*b in the numerator, P0/E1 = 1/r [r - r*b + ROE*b - ROE*b / r - ROE*b] = 1/r [r - ROE*b + ROE*b - r*b / r - ROE*b] or P0/E1 = 1/r [1+ (b(ROE-r) / r - ROE*b)] “This P0/E1 equation is extremely useful because one can use it to examine the effects of different values of b and of the difference between ROE and r, that is, ROE-r. two interesting results can be found. First, if ROE=r, the intrinsic P0/E1 equals 1/r regardless of b, the earnings retention ratio. Second, if b=0, the intrinsic P0/E1 equals 1/r regardless of whether ROE is greater than r. These two results have an intuitive explanation.” “When the return on equity is exactly equal to the required rate of return (ROE=r), there is not added value in retaining earnings for additional investments, rather than distributing them to shareholders. A company with ROE=r has no franchise value potential because its return on equity is just what the market requires, but no more.” “An earnings retention ratio of zero (b=0) means that the company distributes all its earnings. So equity per share stays constant. There is no growth of equity and the stream of future earnings will be a perpetuity because the rate of return on equity (ROE) remains constant. The value of a share is given by discounting a perpetuity of E1 at a rate of r, hence the P0/E1 = 1/r result. Of course, the total equity of the company could grow by issuing new equity, but there will be no growth of earnings per existing share. There is potential franchise vale in the company with ROE>r, but because the company does not reinvest earnings at this superior rate of return, existing shareholders do not capture this potential.” “In general, there is a franchise value created for existing shareholders, if the company can reinvest past earnings (b>0) at a rate of return (ROE) higher than the market-required rate ®.” [simplifying some nasty equations] P0/E1 = 1/r + Franchise Factor*Growth Factor Where the franchise factor = (1/r)-(1/ROE), and growth factor = g/(r-g) [Footnote 17]: The model is derived here under the assumptions of a constant growth rate g, a constant earnings retention rate b, and a constant ROE. It can accommodate more complex assumptions about the pattern of growth. Anyway, that’s most of it. I like how the FF and G clearly show the impact of the relation between r and ROE, and the growth factor demonstrates the impact of the relation between r and g. The end Thank goodness for examples. 2008 LII CFAI Volume IV, Reading 40, p.151: Example 3: Franchise Value A company can generate an ROE of 15% and has an earnings retention ratio of 0.60. Next year’s earnings are projected at \$100M. If the required rate of return for the company is 12%, what ist he company’s tangible P/E value, franchise factor, growth factor, and franchise P/E value? Solution: The company’s tangible P/E value is 1/r = 1/0.12 = 8.33. The company’s franchise factor is 1/r - 1/ROE = 1/0.12 - 1/0.15 = 1.67. Because the company’s sustainable growth rate is 0.6*0.15 = 0.09, the company’s growth factor is g/(r-g) = 0.09/(0.12-0.09) = 3. The company’s franchise P/E value is the franchise factor times the growth factor, 1.67*3 = 5.01. Because its tangible P/E value is 8.33 and its franchise P/E value is 5.01, the company’s intrinsic P/E is 13.34. Note that the intrinsic P/E calculated directly is P/E = (1-b)/(r-g) = 0.4/(0.12-0.09) = 13.33. Thus, the franchise value method breaks this P/E into its basic components.